High-Performance Computing in Geomechanics by a Parallel Finite Element Approach

Okulicka-Dłużewska, Felicja

doi:10.1007/3-540-70734-4_46

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…Coupled problems are common in the real world; description of different mechanical phenomena, such as flow and thermal effects, leads to coupled systems of differential equations. The finite element method (FEM) is widely used to solve such problems, and the most important part of the finite element method algorithm is the procedure for solving the set of linear equations possesing saddle point structure (see [6,10,11]).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of saddle point problems by block {Gram--Schmidt} orthogonalization

Okulicka-Dłużewska¹,

Smoktunowicz²

2013

Preprint

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Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we prove that the algorithm BCGS2 (Reorthogonalized Block Classical Gram-Schmidt) using Householder Q-R decomposition implemented in floating point arithmetic is backward stable, under a mild assumption on the matrix M . This means that the computed vector z is the exact solution to a slightly perturbed linear system of equations M z = f .

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Section: Introductionmentioning

confidence: 99%

Numerical solution of saddle point problems by block {Gram--Schmidt} orthogonalization

Okulicka-Dłużewska¹,

Smoktunowicz²

2013

Preprint

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Solving Coupled Consolidation Equations

Okulicka-Dłużewska

Numerical Methods and Applications

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FEM and BEM parallel processing: theory and applications – a bibliography (1996‐2002)

Mackerle¹

2003

Engineering Computations

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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

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High-Performance Computing in Geomechanics by a Parallel Finite Element Approach

Cited by 3 publications

References 3 publications

Numerical solution of saddle point problems by block {Gram--Schmidt} orthogonalization

Numerical solution of saddle point problems by block {Gram--Schmidt} orthogonalization

Solving Coupled Consolidation Equations

FEM and BEM parallel processing: theory and applications – a bibliography (1996‐2002)

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